1. Field of the Invention
The present invention relates to a resolution-free representation technique.
2. Description of the Related Art
Resolution-free representations of illustrations and texts have conventionally adopted a method of approximating the contour of an object by a Bezier function, spline function, or the like. This method is fast and popular, but is not good at a complicated gradation representation.
In general, a gradient mesh tool available from Adobe Illustrator® is used to render a resolution-free representation of an object containing a complicated gradation. A gradient mesh can render a complicated object by giving a color and gradient to meshes to generate a cubic function (Japanese Patent Laid-Open No. 11-345347 and Japanese Patent No. 4220010).
For a resolution-free representation of an object in a raster image, several methods are proposed to approximate an image using meshes. An example is a method of approximating an image using triangular patches (Japanese Patent No. 3764765). However, this method suffers a problem in the representation of the object boundary. When the object boundary is a smooth curve, it is difficult to approximate the curve faithfully by linear meshes, and a faithful approximation requires many meshes. A high-order mesh is therefore necessary to approximate a complicated boundary using a smaller number of meshes.
As an example of the method using a high-order mesh, Bezier patches are subdivided to reduce an approximation error (Brian Price, William Barrett, “Object-Based Vectorization For Interactive Image Editing”). Another example is a method of approximating an image using a gradient mesh. As a method different from the approximation method using meshes, there is proposed a resolution-free representation method of approximating the feature line of an image by a Bezier curve, adding color information to the two sides of a curve, and solving a partial differential equation using the color of the curve, thereby rendering an image (Alexandrina Orzan, Adrien Bousseau, Holger Winnemoller, Pascal Barla, Joelle Thollot, David Salesin, “Diffusion Curves: A Vector Representation for Smooth-Shaded Images”).
As a method of approximating an image using a gradient mesh, an optimization problem is solved to reduce the approximation error of the gradient mesh (U.S. 2008/0278479). Also, there is proposed a method of dividing an object into triangular meshes, and parameterizing them to generate a gradient mesh (Yu-Kun Lai, Shi-Min Hu, Ralph R. Martin, “Automatic and Topology-Preserving Gradient Mesh Generation for Image Vectorization”).
The use of a high-order mesh allows approximating an object shape with a smaller number of meshes. However, several problems still remain unsolved when faithfully approximating an object color containing a high-frequency component, like a texture. These problems will be described below.
Since the foregoing method of subdividing Bezier patches to reduce an approximation error uses a high-order mesh, the object boundary can be approximated faithfully. However, subdividing meshes to reduce an approximation error increases the number of meshes in a region containing a high-frequency component, and increases the data amount.
The method of approximating the feature line of an image by a Bezier curve can represent the object shape with a small data amount. However, it is difficult to control the color between feature lines, and thus to faithfully represent an object color containing a high-frequency component.
The above-mentioned two methods of approximating an image using a gradient mesh can implement a resolution-free representation using a smaller number of meshes even for an object whose color change is complicated. However, it is hard even for these methods to represent a high-frequency component, like a texture, because the color is rendered by interpolation using a cubic mesh.